5.4 Solving Systems Using Linear Combinations.notebook
October 19, 2011
SECTION 5­4:
SOLVING SYSTEMS USING LINEAR COMBINATIONS
Equations are in
Standard Form
WHEN?
RECALL: Zero solutions if:
One (or 2, 3, 4…)
solutions if:
Equations Parallel
Lines Intersect
Infinite solutions:
Equations are Same Line
5.4 Solving Systems Using Linear Combinations.notebook
October 19, 2011
What happens when variables cancel?
# = #
# = Diff #
Find a solution set for this system using linear
combinations.
Step 1: Decide which variable
to get rid of. Create opposite
coefficients for that variable.
5.4 Solving Systems Using Linear Combinations.notebook
Solve with Linear Combinations
Add Equations Together.
Solve with Linear Combinations
STEP 3. Solve for the variable.
October 19, 2011
5.4 Solving Systems Using Linear Combinations.notebook
Solve with Linear Combinations
STEP 4: Substitute the value back into either of the
equations to solve for the other variable.
B) Find a solution set for this system
using linear combinations.
October 19, 2011
5.4 Solving Systems Using Linear Combinations.notebook
C) Find a solution set for this system
using linear combinations.
AT A RESTAURANT, 4 HAMBURGERS AND 2 FRIES
COST $27.10. AT THE SAME RESTAURANT,
3 HAMBURGERS AND 4 FRIES COST $25.20.
Find the cost of one hamburger and
one fry.
October 19, 2011
5.4 Solving Systems Using Linear Combinations.notebook
October 19, 2011
5.4 Solving Systems Using Linear Combinations.notebook
October 19, 2011
At the zoo, Jay bought 3 slices of vegetable pizza and 1 small lemonade for $4.50. Terri paid $4.80 for 2 slices of vegetable pizza and 2 small lemonades. What is the cost of one small lemonade?
5.4 Solving Systems Using Linear Combinations.notebook
October 19, 2011